Changing the nozzle area changes the combustion chamber pressure. If the pressure upstream is too low, a shock wave will form at some point in the nozzle resulting in subsonic exit flow (and probably causing a fair amount of harm to the nozzle itself). A wider nozzle throat results in lower upstream pressure.

Thanks for the hint. It got me to this, and I'm really enjoying reading it. Cheers..C:

a random excerpt..

Quote

(....) But then Pino, in 1949, made a discovery that can fairly be described as revolting. He discovered that butyl mercaptan was very rapidly hypergolic with mixed acid. This naturally delighted Standard of California, whose crudes contained large quantities of mercaptans and sulfides which had to be removed in order to make their gasoline socially acceptable. So they had drums and drums of mixed butyl mercaptans, and no use for it. If they could only sell it for rocket fuel life would indeed be beautiful.

Well, it had two virtues, or maybe three. It was hypergolic with mixed acid, and it had a rather high density for a fuel. And it wasn't corrosive. But its performance was below that of a straight hydrocarbon, and its odor — ! Well, its odor was something to consider.

Intense, pervasive and penetrating, and resembling the stink of an enraged skunk, but surpassing, by far, the best efforts of the most vigorous specimen of Mephitis mephitis. It also clings to the clothes and the skin. But rocketeers are a hardy breed, and the stuff was duly and successfully fired, although it is rumored that certain rocket mechanics were excluded from their car pools and had to run behind. Ten years after it was fired at the Naval Air Rocket Test Station — NARTS — the odor was still noticeable around the test areas.

California Research had an extremely posh laboratory at Richmond, on San Francisco Bay, and that was where Pino started his investigations. But when he started working on the mercaptans, he and his accomplices were exiled to a wooden shack out in the boondocks at least two hundred yards from the main building.

Undeterred and unrepentant, he continued his noisome endeavors, but it is very much worth noting that their emphasis had changed. His next candidates were not petroleum by-products, nor were they chemicals which were commercially available. They were synthesized by his own crew, specifically for fuels. Here, at the very beginning of the 50's, the chemists started taking over from the engineers, synthesizing nc:w propellants (which were frequently entirely new compounds) to order, instead of being content with items off the shelf.

Anyhow, he came up with the ethyl mercaptal of acetaldehyde and the ethyl mercaptol of acetone, with the skeleton structures:

respectively. The odor of these was not so much skunk-like as garlicky, the epitome and concentrate of all the back doors of all the bad Greek restaurants in all the world.

And finally he surpassed himself with something that had a dimethylamino group attached to a mercaptan sulfur, and whose odor can't, with all the resources of the English language, even be described. It also drew flies. This was too much, even for Pino and his unregenerate crew, and they banished it to a hole in the ground another two hundred yards farther out into the tule marshes.

Some months later, in the dead of night, they surreptitiously consigned it to the bottom of San Francisco Bay...

If the pressure upstream is too low, a shock wave will form at some point in the nozzle resulting in subsonic exit flow.

Interesting. Would you mind going a bit more into the detail as for the conditions needed for this to happen (or to avoid it)?

In the case of an ideal gas flowing through an ideal nozzle, the pressure drops by a factor of [(k + 1) / 2]k/(k - 1) from the nozzle entrance to the throat, k being the ratio of the specific heat at constant pressure to that at constant volume (see a textbook like Sutton's Rocket Propulsion Elements). If the ambient pressure is higher than the pressure at the throat (the nozzle exit in a converging-only nozzle), you won't get supersonic flow. A representative value of k is 1.2, so the chamber pressure needs to be at least 1.8 times ambient. In a real nozzle with a non-ideal gas, the pressure would need to be a little higher.

My reference to nozzle exit pressure was in the context of a converging-only nozzle, which makes sense in the context of ScepticMatt's question. I absolutely guarantee that the pressure at minimum cross-section of the SSME (ie, the throat) is much greater than atmospheric.

Antares 100 cores (the ones with the NK-33) used subcooled LOX because it was required by the NK-33. Dr. Elias has stated here that he desired to do away with it, but given that the 200 cores are re-engined 100 cores, if they didn't subcool they will loss propellant mass. Given that the 300 cores (the ones designed for the RD-181) have increased propellant load, one would assume that they will keep using the subcooled LOX until the 300 cores.

Bumbling about the internet today, I saw someone say that the Antares and the Soyuz 2-1v used LOX at different temperatures (even though they use the same base NK-33 rocket engine), which made me wonder how much of a density difference the engine can handle.

Soyuz 2-1v (-192°C)Antares (–196°C)

However, I could not find a density chart for liquid oxygen at different temperatures. I had to dig up an online calculator to work this out and I'm not certain of its accuracy. Can anyone help me out with this?

LOX at -192 C = 736.62 kg/m3LOX at -196 C = 979.81 kg/m3

Is this correct? It seems like an enormous leap in density.

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Liquid oxygen at 25C is under extreme high pressure and may not be representative of cryogenic liquid oxygen: coefficient of thermal expansion in real substances is not perfectly fixed over all temperatures.

1204 to 1185 kg/m3 for that shift, or a 1.6% difference. There's some small pressure dependence, but it's negligible at these temperatures and realistic tank pressures (~.1 kg/m3 difference for 30 vs 50 psia).

"One bit of advice: it is important to view knowledge as sort of a semantic tree -- make sure you understand the fundamental principles, ie the trunk and big branches, before you get into the leaves/details or there is nothing for them to hang on to." - Elon Musk"There are lies, damned lies, and launch schedules." - Larry J